Question: Simplify the following expression: $k = \dfrac{2g^2 + 6hg}{6g^2 + 2hg} - \dfrac{4fg + 8g^2}{6g^2 + 2hg}$ You can assume $f,g,h \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{2g^2 + 6hg - (4fg + 8g^2)}{6g^2 + 2hg}$ $k = \dfrac{-6g^2 + 6hg - 4fg}{6g^2 + 2hg}$ The numerator and denominator have a common factor of $2g$, so we can simplify $k = \dfrac{-3g + 3h - 2f}{3g + h}$